Corkscrew or streching an ellipse

[CVH]

Nice, thank you ...
Probably the best solution up to now.
You have to admit that what Chips&Chips presented on Feb 29 comes very close visually.
I don't think that it must be exact for the intended purpose ...

One of the problems I see is that in QCAD splines end normal.
Your start and end curvature is thus not entirely correct between the last 2-3 fitpoints at either side.
Solution:
Overdo it at least 2 extra points at both ends and trim the fit-point spline at the Y axis.
That will result in a control point spline with proper end tangents.

An unanswered question is rendering load.
How much more lag do 8 splines of degree 3 induce compared to 16 ellipses and that for numerous helix blocks inserted on drawing?

And how does that compares with your final spline with 193 fit-points (8x24+1)?
Selecting a 10 by 10 array of such blocks takes about 2-3 seconds on my old Pentium 7.
Some quick test tells me that the spline block is faster ...

Last question:
What type of projection is this?
https://en.wikipedia.org/wiki/3D_projection
Your X axis is horizontal and both your Y and Z axis are vertical ...

Regards,
CVH

[DerekGove]

Nice, thank you ...
Probably the best solution up to now.

- Cheers. you're welcome. I'm sure some clever person could write a script to do the same thing, but that's how a 3D view of a helix should be constructed— with pencil and paper at least. And it's easy enough to use in cases where a "Draw helix in 3D" button doesn't exist. :

You have to admit that what Chips&Chips presented on Feb 29 comes very close visually.
I don't think that it must be exact for the intended purpose ...

- Yeah, totally agree. His solution was nice visually, and looked good for a diagramatical representation. Certainly a nicer result than the traditional simplified version of a helix...
edit: Worth noting that the original poster, sancyk, was asking about a helix in isometric, so I hope this has been helpful for them, even though Chips&Chips may not have needed an accurate solution.

Springs2.png (159.46 KiB) Viewed 173 times

Springs1.png (82.65 KiB) Viewed 173 times

And these aren't even in 3D. LOL

One of the problems I see is that in QCAD splines end normal....

-Yeah. If I was doing something where I wanted the end tangents correct, I'd add an extra revolution on each end, and then cut them off where I needed.

An unanswered question is rendering load.
...
Some quick test tells me that the spline block is faster ...

- Well, I'm not running QCAD on a Pentium 7, so you're in a better position to judge that. But looking at the traditional 'simplified' helix, this method could even be massively simplified to a dozen, or even fewer straight lines per rotation. Depends how detailed a diagram or representation needs to be, and how prominently the helix will feature.

Simplified-helices.png (9.52 KiB) Viewed 173 times

Here's one with 8 lines per rotation (not even a spline), which would be acceptable in certain circumstances, and another with only 4 lines per rotation, which is about as bare-bones as you can get. It'll render really, really fast, but I don't think even I'd use it except under duress.
I only really threw these together to illustrate that the construction can be as detailed or as simple as required.

Last question:
What type of projection is this?
https://en.wikipedia.org/wiki/3D_projection
Your X axis is horizontal and both your Y and Z axis are vertical ...

- That last one in my original post was a dimetric projection. (I'd have normally done an example in isometric, but I wanted to try and match the spacing in Chips&Chips' drawing, so 'reverse engineered' the minor axis of the ellipse to match)
In both dimetric and isometric, once the view is rotated 45 degrees and then foreshortened, it is still a perfect ellipse, (as there is no perspective distortion) so it doesn't matter that it was drawn in such a way that it appeared that the x, y and z axes were horizontal and vertical. In Chips&Chips' drawing, he had the starting point of the helix 'front and centre', so I did my drawing to match that.
Here's the standard construction (with an unneccessary bounding square added for clarity), and it converted into isometric.

ISO-circle1.png (14.32 KiB) Viewed 173 times

As you can see, there isn't a 30/60 line intersecting the ellipse at a point where I wanted it, at the lowest point of the circle.

So if I rotate the circle and lines by 45 degrees first, and then convert/foreshorten it for isometric, The ellipse is identical, but this time I have my construction lines exactly where I want.
edit: Worth noting too, that as I ended up using a circle divided into 24 parts, not the 12 I would use if drawing one by hand, there's no need to rotate it 45 degrees at all.

ISO-circle2.png (14.52 KiB) Viewed 173 times

Planometric drawings are easy, because the 'top' view is a perfect circle anyway.
For auxiliary projections, trimetric, cavalier or cabinet, (and I were doing it by hand) I'd probably use the enclosed parallellogram method to locate my key points for my base circle that I project the helix up from:

EnclosingParallellogram.png (18.23 KiB) Viewed 173 times

But of course, QCAD has some great built in functions to convert orthographics into those types of drawings.

Cheers,
Derek